I know it's stressful for owners to watch and it's easy get upset. Honestly, I would have them take her to the back next time so you don't have to watch. If you get upset, she is going to get more upset. Trying to poke around for a vein under the skin for an extended period isn't good, so maybe a different tech can do it next time. Techs do it much more than vets though, so the vet may or may not be any better at it... Small dogs gets draws exclusively out of the jugular here. It isn't always easy to draw from a small dog. Not really sure why some vets do it in front of owners. They always go to the back here. Anyway, they may have had an easier time finding the jugular.
She will be fine. No worries.